Mathematics - Permutation & Combination Question with Solution | TestHub

Choose the three range elements. Counting derangements on the retained elements and the repeated image gives $\left(\genfrac{}{}{0ex}{}{4}{3}\right)[D(3)\left(\genfrac{}{}{0ex}{}{3}{1}\right)+$ $\left(\genfrac{}{}{0ex}{}{3}{2})D(2)\cdot 2\right]=4(6+6)=48$. Hence $k/12=4$.